Phenomenological description of grain growth stagnation for nanocrystalline films and powders

We provide a phenomenological grain growth stagnation force incorporating a near-linear temperature dependence of stagnated grain sizes and irreversible growth. The resulting law captures the observation of the restart of grain growth in the size versus time plateau on temperature increases. This description also reduces to standard laws commonly used for data fitting. The law may be useful for workers who wish to characterize a nanocrystalline film or powder annealing process predictively from a limited number of measurements or may be useful in a designed experiment. Other laws are discussed and compared. Fits to size versus time data from the literature are successfully made.